Geometric Derivation of Malus's Law from Structured Vacuum Theory: Eliminating the Photon Paradox

This paper presents a first-principles derivation of Malus's law (I = I₀ cos²θ) directly from the Structured Vacuum Theory (TVS) Lagrangian without free parameters. Polarization emerges as geometric filtering of torsional wave components by anisotropic V23 channel alignment in materials, not as quantum superposition of photon states. We demonstrate that: The three-polarizer experiment—inexplicable with classical particles—follows trivially from vector projection of torsional waves Continuous polarization angles arise naturally from the vector nature of torsion field τ, requiring no discrete spin-1 particles The derivation yields unique falsifiable predictions: 23-fold anisotropy in photoelectric thresholds and modified Verdet constant in Faraday rotation TVS resolves the ontological paradox of photons having discrete spin (±ħ) yet exhibiting continuous polarization angles. All results emerge from vacuum geometry: 23-channel dodecahedral structure (V23) with fundamental length λ₀ ≈ 1.2×10⁻¹⁰ m.